The Mechanism of the Med vie Arc. 



411 



pit, hence it remains concave. When the arc is long, the burning of 

 the sides gains over the volatilisation of the centre, and the surface of 

 volatilisation becomes flat, or even slightly convex. 



The peculiar shaping of the negative carbon is shown to be due to 

 its tip being protected from the air by the mist, and its sides being 

 burnt away under the double action of radiation from the vapour 

 film and conduction from the mist, to a greater or less distance, 

 according to the length of the arc and the cross-section of the vapour 

 film. 



It is shown that if the crater be defined as being that part of the 

 positive carbon that is far brighter than the rest, then the crater must 

 be larger, with the same current, the longer the arc, although the area 

 of the volatilising surface is constant for a constant current. 



By considering how the cross-section of the vapour film must vary 

 with the current and the length of the arc, it is found that its 

 resistance /, must be given by the formula 



, _ h 1c + ml 

 f ~ A + ^P"' 



where h, k s and m are constants, I is the length of the arc, and A the 

 current. This is the same form as was found by measuring the P.D. 

 between the positive carbon and the arc by means of an exploring 

 carbon, and dividing the results by the corresponding currents. Hence 

 the existence of a thin film of high-resisting vapour in contact with the 

 crater would not only caus e a large fall of potential between the 

 positive carbon and the arc, exactly as if the crater were the seat of a 

 large back E.M.F., but it would cause that P.D. to vary with the 

 current and the length of the arc exactly as it has been found to vary 

 by actual measurement. 



The Apparent " Xegative Resistance." 



As nearly all the current flows through the vapour and mist, the 

 surrounding flame being practically an insulator, the resistance of a 

 solid carbon arc, apart from that of the vapour, must depend entirely 

 on the cross-section of the mist. To see how this varies with the 

 current, images of an arc of 2 mm. were drawn, with the purple 

 part — the mist— very carefully defined, for currents of 4, 6, 8, 10, 12, 

 and 11 amperes. The mean cross-section of the mist was found to 

 increase more rapidly than the current, consequently its resistance 

 diminishes more rapidly than the current increases. As the formula 

 for the resistance of the vapour film shows that it too diminishes faster 

 than the current increases, it follows that the whole resistance of the 

 -arc does the same, and that consequently the P.D. must diminish as the 

 •current increases. Hence if SV and oA be corresponding increments of 



